Lilavati (Bhaskaracharya) (1800) - Page 20

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Determining Variations in the Gayatri Meter

Verse:
O friend, tell me how many variations of the Gayatri a Vedic meter consisting of six syllables per verse-quarter exist in a permutation Prastara: a systematic expansion of all possible combinations of long and short syllables, and how many of those possess one heavy syllable Guru: a long syllable, often represented by the number 2 or a curved line and so on. Explain the method.

11. Here, the Gayatri verse-quarter consists of six syllables. Therefore, to find the variations, place the numbers one to six in increasing and decreasing order for the arrangement:

6 1 5 2 4 3 3 4 2 5 1 6

This represents the fractions 6/1, 5/2, 4/3, 3/4, 2/5, and 1/6 used to calculate combinations (6 choose 1, 6 choose 2, etc.)

By following the prescribed calculation:
1. The variations with one heavy syllable are obtained as 6 calculated as 6 divided by 1.
2. Multiplying this 6 by the next number [5] equals 30; divided by the next divisor [2], the result is 15, which are the variations with two heavy syllables.
3. By this same process, three heavy syllables result in 20 (15 × 4) / 3 = 20.
4. Four heavy syllables result in 15 (20 × 3) / 4 = 15.
5. Five heavy syllables result in 6 (15 × 2) / 5 = 6.
6. Six heavy syllables result in 1 (6 × 1) / 6 = 1.

Just as there is only one variation where all syllables are heavy, there is also only one variation where all syllables are light Laghu: a short syllable.

Thus, the total measure of variations for a single verse-quarter is 64 The sum of 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64, which is 2 to the power of 6. In this way, one should consider the numbers of variations... having calculated the individual differences for one heavy syllable and so on, their sum total for the Gayatri meter is 64 3? 216 The number 216 here likely refers to a different calculation or a scribal error, as 64 is the standard total for a 6-syllable line.

This method for knowing the measure of variations applies to all meters, from Ukta the simplest meter with 1 syllable to Utkriti a complex meter with 26 syllables. For example, tell me, O King, the variations for meters starting with one, two, or three syllables... of gold... beautiful... twenty-four...